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Often ISPs will allow an open relay from internal IP address since they can monitor things and make sure people aren't abusing them. But doing it that way can cause delivery problems as well for some email servers.. if a receiving server see the email address it's coming from as being @telus.net but the IP address is @shaw.ca then the email server will reject the email or flag it as spam or something. Maybe some of the ISPs do something behind the scenes to help with that kind of thing with each other to improve deliverability when people move over.

But in general H&L is correct, having an open SMTP relay (which is what you're describing, an SMTP server that will accept incoming emails from anywhere and send them) is a bad thing (tm). If they exist they usually are for use for spamming and are quickly blacklisted or shut down.

Anyway, whatever email address domain your uncle is using, there should be an externally accessible SMTP server that requires authentication that can be used to send emails through no matter where they are. It used to be that ISPs didn't provide external access to their SMTP servers, but that was a long time ago I think they all do now.

What's the domain name for his email address?

Incidentally this is why I'm a fan of having your own domain name for emails, that way the email address can be moved to different services or providers without issue.